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Transformations: y = a f(k(x − d)) + c
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Learn it In y = a f(k(x − d)) + c: |a| stretches vertically (a < 0 reflects in the x-axis); |k| compresses horizontally by 1/k (k < 0 reflects in the y-axis); d shifts right; c shifts up. A point (x, y) moves to (x/k + d, ay + c). Do stretches and reflections before translations.
Example: (4, 6) is on y = f(x). Find its image on y = 2f(½(x − 1)) + 3.
- x: 4 ÷ ½ + 1 = 9.
- y: 2(6) + 3 = 15.
- (9, 15).
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